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Tytuł artykułu

Morley’s Trisector Theorem

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Wydawca
Rocznik
Tom
23
Numer
2
Strony
75-79
Opis fizyczny
Daty
wydano
2015-06-01
otrzymano
2015-03-26
online
2015-08-13
Twórcy
  • Rue de la Brasserie 5 7100 La Louvière, Belgium
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [3] Alexander Bogomolny. Morley’s miracle from interactive mathematics miscellany and puzzles. Cut the Knot, 2015.
  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [5] Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.
  • [6] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [7] Roland Coghetto. Some facts about trigonometry and Euclidean geometry. Formalized Mathematics, 22(4):313-319, 2014. doi:10.2478/forma-2014-0031.
  • [8] Alain Connes. A new proof of Morley’s theorem. Publications Math´ematiques de l’IH ´ES, 88:43-46, 1998.
  • [9] John Conway. On Morley’s trisector theorem. The Mathematical Intelligencer, 36(3):3, 2014. ISSN 0343-6993. doi:10.1007/s00283-014-9463-3.
  • [10] H.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967.
  • [11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • [12] Cesare Donolato. A vector-based proof of Morley’s trisector theorem. In Forum Geometricorum, volume 13, pages 233-235, 2013.
  • [13] O.A.S. Karamzadeh. Is John Conway’s proof of Morley’s theorem the simplest and free of A Deus Ex Machina ? The Mathematical Intelligencer, 36(3):4-7, 2014. ISSN 0343-6993. doi:10.1007/s00283-014-9481-1.
  • [14] Akihiro Kubo and Yatsuka Nakamura. Angle and triangle in Euclidean topological space. Formalized Mathematics, 11(3):281-287, 2003.
  • [15] A. Letac. Solutions (Morley’s triangle). Problem N 490. Sphinx: revue mensuelle des questions r´ecr´eatives, 9, 1939.
  • [16] Eli Maor and Eugen Jost. Beautiful geometry. Princeton University Press, 2014.
  • [17] Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455-460, 2001.
  • [18] Cletus O. Oakley and Justine C. Baker. The Morley trisector theorem. American Mathematical Monthly, pages 737-745, 1978.
  • [19] Marco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16 (2):97-101, 2008. doi:10.2478/v10037-008-0014-2.
  • [20] Brian Stonebridge. A simple geometric proof of Morley’s trisector theorem. Applied Probability Trust, 2009.
  • [21] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
  • [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [24] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_forma-2015-0007
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